Multivariate time series are, to the best of my understanding, one of the few cases where Deep Learning still hasn't had its AlexNet moment. I'm especially interested to the case where most of the time series are continuous variables, with a few being categorical variables. To fix the ideas, think sensors of a big industrial machine - some sensors will record real-valued time series (pressure, temperature, speed, etc.) and some other categorical time series ("running/non running", "alarm 1/alarm 2/ no alarm", valve open/ valve closed", etc.). If the introduction of categorical variables makes the problem too hard, no issues - we can consider only continuous variables.
Some of these time series have a lot of missing data (the norm, rather than the exception, in industry) and I'd like to perform missing value imputation. In theory, a generative model seems the perfect fit for such a problem, thus I thought of VAEs. In practice, all the applications of VAE to missing data imputation that I know of, are related to images. Never seen them applied to missing data imputation for multivariate times series.
Can they be used? If so, which is the major modification I need to make to the architecture, in order to get a performing implementation for my use case? If no, which other Deep Learning or AI model are suitable for missing data imputation with multivariate time series?